The present invention generally relates to a process control method. More particularly, the invention is directed to a process control system for controlling a process exhibiting both linear and non-linear behavior. The control is performed by a combination of control quantities for plural control effectors including a plurality of digital or analogue quantities.
In recent years, approaches for application of the fuzzy theory to actual processes on a real time basis have been vigorously studied in the field of control techniques and some practical applications have been reported. The basic concept of fuzzy theory is based on the point that "a theoretical system established definitely can not exceed a certain boundary or circumscription". Therefore, behavior of an actual process which includes non-linear elements can not be controlled in a satisfactory manner using only a control method which relies on mathematical expressions which represent physical models. Introduction and application of fuzzy theory to control systems may be explained by the fact that because of very large scale and complex implementation of modern control systems, extreme difficulty is encountered in making available the accurate information required for computer processing in the present state of the art. As a scale of the control system becomes larger, the number of non-linear elements increases correspondingly, making it impractical or impossible to describe the process accurately with mathematical expressions. Under such circumstances, any fuzziness accompanying the action taken by an operator action in the process control system assumes an important role in the process control.
In the following, some examples of control systems relying upon the conventional control procedure based on mathematical models and applied fuzzy theory will be discussed to make clear the problems to be coped with by the present invention.
As a typical example of a conventional control system based on mathematical models and including a large number of non-linear elements and lots of fuzziness, let's consider a longitudinal flow type ventilation control system adopted in the management of a huge tunnel having a great length.
Construction of rapid transit roadways flourished in recent years and includes the construction and use of long tunnels in an increasing number. Also in the future, it is expected that the number of long tunnels will increase for many reasons such as the need for exploitation of the shortest route to a destination, difficulty in acquisition of a site for the construction and progress in civil engineering technology.
In connection with operation and use of a tunnel for a transit roadway, ventilation equipment is required in order to protect car drivers from the danger of exhaust gases and ensure the safety of persons engaging in maintenance. In conjunction with the ventilation for a long tunnel, although a transverse type ventilation system employing ventilation ducts installed in the extending direction of the tunnel have been employed in many cases because of high performance ventilation, a longitudinal type ventilation system including a combination of jet fans (blowers) and dust/dirt collectors is has taken on the leading role in recent years because of low cost of installation and facility of maintenance.
In either one of the ventilation systems mentioned above, the most important problem is how to satisfy the requirements imposed on the running cost of the ventilation equipment on one hand and the quality of ventilation on the other hand. Such requirements or conditions being in a reciprocal relationship. Heretofore, problems of non-linearity (uncertainty) involved in the prediction of a turbulent diffusion phenomenon and a pollution genesis mechanism inherent to the tunnel ventilation process have been dealt with only by linear control relying on mathematical models. Accordingly, a satisfactory control result can be obtained only when the ventilation process exhibits linearity. If otherwise, the control process can not afford a satisfactory result.
FIG. 2 of the accompanying drawings is a conceptual view illustrating control factors in a longitudinal type long tunnel ventilation control system. Jet fans or blowers 7 and dust collectors 8 constituting parts of the ventilation equipment controlled by a control apparatus 1. They are indispensable members playing an important role in retaining the concentration of pollution gases such as CO, NO.sub.s, SO.sub.x and others noxious to the human body and smog harmful to the safety of the drive. Since the electric power consumed by these jet fans and the dust collectors is a large proportion of the electric power consumption of the whole tunnel, there exists a strong demand for efficient operation of these facilities. In other words, the tunnel ventilation control has to satisfy simultaneously two contradicting requirements, i.e. safety and economy, as mentioned above. As a control system adopted in the practical application for coping with the above requirements, there is a so-called traffic flow prediction feed-forward control system.
FIG. 3 of the accompanying drawing is a view illustrating the principle underlying the traffic prediction feed-forward control system mentioned above. For expressing the tunnel ventilation process in the form of a mathematical model, the tunnel is divided into n sections by taking into consideration conditions such as slope, the positions where the ventilation machines are installed and other factors. For this purpose, the state within each section for ventilation can be expressed by a difference equation mentioned below. ##EQU1## where X(k+1) represents an average concentration of pollution within a ventilation section of concern at a time point K(t=kT), P(k) represents an amount of pollution generated within the ventilation section of concern during a period k(kT.ltoreq.t.ltoreq.(k+1)T), and Q(k) represents ventilation airflow within the ventilation section of concern during a period k(kT.ltoreq.t.ltoreq.(k+1)T).
When a standard or reference pollution quantity generated within the tunnel of concern is represented by P* with Q* representing a reference ventilation flow quantity for maintaining a reference pollution concentration X* corresponding to the quantity P*, there can be derived from the expression (1) the following expression: EQU Q*=P*/X* (2)
For determining a corrected ventilation when the concentration of pollution X(k) and the generated pollution quantity P(k) at the current time point k deviate from the respective reference quantities, variations between the actual quantities and the associated reference quantities are defined as follows: ##EQU2##
By substitution of the expressions (3) in the expression (1) and through linear approximation in the neighborhood of the reference quantity, there can be obtained the following system equation: EQU .DELTA.X(k+1)=exp(-Q*).multidot..DELTA.X(k)-(1-exp(-Q*)) (.DELTA.Q(k)-.DELTA.P(k)) (4)
In the above equation, considering .DELTA.X(k) as representing a state variable, .DELTA.Q(k) as representing a control variable and .DELTA.P(k) as representing an input variable, there can be realized a quantitative expression for the system. However, what is expressed by this equation is only a few of the process behaviors, as will hereinafter be made clear. For configuring the control system, it is required at the next stage to introduce an objective function. At this juncture, it is presumed that the object of the ventilation control mentioned above is to decrease the electric power consumption to a minimum while maintaining the concentration of pollution at the reference or standard level as far as possible. This presumption can be expressed in the form of a function as follows: ##EQU3## In the above expression, the first term of the left-hand side concerns the safety and the second term concerns the economy, wherein F.sub.X and F.sub.Q are the coefficients for adjusting the weight assigned to these terms, respectively. In accordance with a known linear regulator theory, the corrected ventilation airflow .DELTA.Q.degree. (k) which minimizes the objective function given by the expression (5) can be determined from the system equation as follows: EQU .DELTA.Q.degree.(k)=G.sub.X (k).multidot..DELTA.X(k)+.DELTA.G.sub.P (k).multidot..DELTA.P(k) (6)
where G.sub.X (k) and G.sub.P (k) represent feedback gains for .DELTA.X(k) and .DELTA.P(k), respectively.
A control system realized through repetition of the linear approximation procedures described above is shown in FIG. 4. Assuming in this control system that the concentration quantity (the level of the concentration) X(k) at a time point k can be determined accurately on the basis of a pollution sensor, it is believed that the improvement of the control accuracy will then depend only on the improvement of accuracy with which the traffic at a time point (k+1) can be predicted, because ##EQU4## where c.sub.j represents the amount of pollution generated by one motor vehicle of type j, and n.sub.j (k) represents the traffic amount (the number of motor vehicles) during the period k(kT.ltoreq.t.ltoreq.(k+1)T) on the assumption that the amount of pollution generated is in proportion to the number of motor vehicles or cars transited during the period k. In this regard, a prediction of the car transit number (i.e. the number of the cars transited during the period k) can be carried out, for example, by installing traffic counter sensors (hereinafter also referred to as TC) at the entrance and the exit of a tunnel, respectively, and by taking advantage of the fact that a linear relation exists in covariance among the time-series traffic data for the tunnel section of concern. Now, examples of the actually performed control based on the traffic prediction feed-forward control principle will be described with reference to FIGS. 5 to 7 of the accompanying drawings.
FIG. 5 shows transitions in the traffic and pollution quantities, respectively, during an elongated control period, i.e. when the ventilation airflow is made approximately constant. As will be seen from the graphs, there exists high correlation between the traffic quantity and the amount of pollution as produced. Further, the graphs show that the environment standard value (80 ppm in the case of the illustrated example) has been exceeded several times, indicating a low quality or performance of the ventilation (degraded safety). On the other hand, in the case of the control illustrated in FIG. 6 where the traffic prediction feed-forward control has been performed for a period of ten minutes, the concentration value of CO converges to the objective value. Further, it can be seen that the electric power consumption is also improved when compared with the example shown in FIG. 5.
FIG. 7 illustrates, by way of example, the situation existing in the middle of the night where the traffic rate is low during a period of the same duration. Although it is obvious from the graphs that the ventilator operation is not required because the traffic is low, the ventilator is thrown into operation several times, consuming a large amount of electric power. The actual operation of the system adopting the traffic prediction feed-forward control will be what is mentioned below. On the basis of empirical knowledge, the operator usually takes the following procedures:
(1) In the middle of the night, the operator changes over the automatic operation control to manual operation control on the basis of judgment of the total traffic quantity and the rate of change thereof. This manual operation control is continued into the rush-hour which occurs in the morning. PA1 (2) In case the change in the traffic flow is remarkable even in the daytime, such as on a holiday, the control is changed over to the manual operation control. PA1 (3) On a rainy day, the manual operation control is performed at a lower value than the controlled ventilation quantity outputted from the automatic control operation system, and so forth. PA1 (1) An inference main mechanism in which a linear control system is provided for dealing with the linear behaviors of a process while a qualitative inference control system is provided for processing the non-linear behaviors of the process, wherein a decision as to linear/non-linear behaviors is realized by a forward fuzzy inference performed on the basis of empirical knowledge; PA1 (2) a complex fuzzy inference mechanism for a many-faceted grasp of process behaviors is provided by examining in a composite manner different types of factors through cooperation with the qualitative inference mentioned in the above paragraph (1); PA1 (3) a predicting fuzzy inference mechanism for determining operations of the control effectors is provided by examining in a composite manner different control objectives on the basis of the result of a decision made for the process behaviors mentioned in the paragraph (1); and PA1 (4) a process control method is provided for performing automatically a continuous control in correspondence to the behaviors of a process with the aid of a complex inference mechanism including the mechanisms (1), (2) and (3) mentioned above.
As will be seen, specific operations are performed through intervention by the operator in accordance with various rules established empirically by the operator. Considering the traffic control in terms of a general process control, there exist various situations in which the process behaves linearly, utterly non-linearly and partially linearly, respectively. This can be explained by the fact that an attempt has been made to handle the non-linear components in the various controls by a linear equation including the external disturbance elements. Accordingly, when the external disturbance becomes a leading factor in the process behavior, there arises the necessity for another system description. In general, the control system such as a tunnel ventilation control, includes many elements or components which have a fuzzy control description. Besides, these elements compete with one another for control of the process behavior from time to time. For these reasons, the quantitative expressions of these disturbance elements are very difficult to define.
FIG. 8 shows in a network diagram the main causes or factors for the pollution produced within a tunnel as confirmed by resorting to all the conceivable means, such as simulation, actual measurements and others. As can be seen in the figure, there are more than twelve causes or factors affecting the environment as a result of pollution, inclusive of the medium factors. All of these factors are of such a nature that they behave linearly at one time and non-linearly at another time. Besides, these factors may bear a relation to one another at one time, while no relation can be found at another time.
FIG. 9 shows in a network diagram similar to FIG. 8 the factors or causes participating in the ventilation. As can be seen in the figure, a weather phenomenon, such as natural airflow plays an important role as well.
As will now be appreciated from the foregoing description, the serious problem of the hitherto known ventilation control system based on a mathematical model can be seen in that the ventilation control system can no longer be used tolerably except for the period during which all the factors behave linearly, as is discussed in detail in an article entitled "A New Ventilation Control For Long Road Tunnel" contained in a collection of articles and reports published in the Japan Society of Civil Engineers, No. 265 (1977).
In contrast to the control based on a mathematical model as described above, fuzzy control is characterized in that the behaviors of factors affecting a process are expressed in terms of fuzzy quantities, wherein the final control quantities to be outputted are derived by transforming the fuzzy values having proper acceptance into quantitative values. However, the fuzzy control known heretofore suffers from shortcomings as mentioned below.
First, a large number of items exist for the fuzzy evaluation, wherein evaluation for deriving a conclusion (operation control quantity) from the items is not only impractical but also difficult to understand.
Another disadvantage lies in that fuzzy control may become more ineffective than control based on a linear control model, depending on the situations, because control based on fuzzy quantities are applied even to a process phase which can be controlled with a high accuracy by the conventional linear model based control. This can be explained by the tendency that a process subject to the control is grasped definitely either as a process oriented for fuzzy control or as a process suited for linear control. The prior art fuzzy control is disclosed in detail, for example, in JP-A-58-19207 and JP-A-59-204707.
It is safe to say that processes in the real world are, more or less, extremely complicated combinations of linear behaviors, and non-linear behaviors and thus it is impossible to realize an optimum control for all situations with one definite control procedure.